6 from 49 lottery odds calculator
A 6 from 49 draw has 13,983,816 equally likely outcomes, so a single ticket wins the jackpot with probability one in that number. The combinatorics are computed as exact integers. The classic format, used by Lotto 6/49 in Canada and many European draws.
- Possible draws
- 13 983 816
- Chance of winning
- 0.000 007 151 12 %
- Expected value of the ticket
- -1.78
- Jackpot at which the bet breaks even
- 34 959 540.00
- Annual cost of playing every draw
- 260.89
- Chance of a jackpot in a year
- 0.000 007 462 68
- Years for an even chance
- 92 881.4
- Your share in a syndicate
- 1 000 000.00
- Syndicate odds: one in
- 1 398 382
Show the working
- Tickets bought = 1
- Ticket price = 2.5
- Jackpot = 10 000 000
- Draws per week = 2
- Syndicate members = 10
- Possible draws = comb(49, 6) = 13 983 800
- probability = 13 983 800 > 0 ? 1 / 13 983 800 : 0 = 7.15112e-8
- Odds: one in = 7.15112e-8 > 0 ? 1 / 7.15112e-8 : 0 = 13 983 800
- Chance of winning = 7.15112e-8 * 100 = 0.000 007 151 12
- Expected value of the ticket = 7.15112e-8 * 10 000 000 - 1 * 2.5 = -1.784 89
- Jackpot at which the bet breaks even = 7.15112e-8 > 0 ? 1 * 2.5 / 7.15112e-8 : 0 = 34 959 500
- Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
- Chance of a jackpot in a year = 1 - (1 - 7.15112e-8)^(2 * 52.17857142857143) = 0.000 007 462 68
- Years for an even chance = 7.15112e-8 > 0 ? ln(0.5) / ln(1 - 7.15112e-8) / (2 * 52.17857142857143) : 0 = 92 881.4
- Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
- Syndicate odds: one in = 13 983 800 > 0 ? 13 983 800 / (1 * 10) : 0 = 1 398 380
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- combinations = C(49, 6)
- probability with n tickets = n / combinations
- expected value = probability x prize - cost
Expected value ignores the smaller prize tiers and any rollover sharing. A positive expected value does not make a lottery a good investment, because the variance is enormous.
Buying more tickets multiplies your chance linearly, but so does the cost. Nothing about the odds improves per pound spent.
These are exact integer combinations, not rounded figures.
The classic format, used by Lotto 6/49 in Canada and many European draws.
6 from 49 odds at a glance
| Tickets | Odds of the jackpot |
|---|---|
| 1 | 1 in 13,983,816 |
| 10 | 1 in 1,398,382 |
| 100 | 1 in 139,838 |
| 1,000 | 1 in 13,984 |
| 10,000 | 1 in 1,398 |
Frequently asked
What are the odds of winning 6 from 49?
One in 13,983,816 per ticket.
Do quick picks have better odds?
No. Every combination is equally likely. Choosing unusual numbers only changes how many people you would share a jackpot with.